what dac to use with iPod and home stereo system

I have my iPod touch connected to my home stereo using the headphone jack and a simple 1/8" stereo TRS to RCA plugs cable. I've read that a DAC can improve the sound quality but most of the less expensive ones seem to be designed for headphones. I assume an external DAC would take the signal from the Lightning socket. Is this correct? I also have an iPhone 11 and would like to be able to use this with the home stereo. What economical (under $200) DAC would you suggest?